The Role of Equivalence Ratio Oscillations in Driving Combustion

Instabilities in Low NOx Gas Turbines*

Tim Lieuwen and Ben T. Zinn

Schools of Mechanical and Aerospace Engineering

Georgia Institute of Technology

Atlanta, GA 30332

27th International Symposium on Combustion

August 1998

University of Colorado at Boulder

____________________________________________________________________

* Research supported by U.S. Dept. of Energy

Combustion Instabilities in Low NOx Gas Turbines

• Modern gas turbines operate in a lean, premixed mode of combustion to reduce NOx emissions

• Key problem - occurrence of detrimental combustion instabilities

• Need to understand mechanisms responsible for these instabilities

Dependence of Heat Release Rate on Equivalence Ratio

Release heatof Rate• Chemical time increases rapidly as the equivalence ratio ()

decreases.

• Quantitative Analysis - Fluctuation in reaction rate increases by 2 orders of magnitude as decreased

– Lieuwen, T., Neumeier, Y., Zinn, B.T., Comb. Sci. and Tech, Vol. 135, 1-6, 1998.

From ZukoskiAerothermodynamics of Aircraft Gas Turbine Engines, 1978

chem1/ Rate

Reaction

Release

Heat

of Rate

0

0.0005

0.001

0.0015

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9Equivalence Ratio

Cha

ract

eris

tic Ig

nitio

n Ti

me,

ms

A Mechanism for Combustion Instabilities due to Oscillations

Heat Release Oscillations

AcousticOscillationsin Inlet andFuel Lines

Equivalence Ratio

Fluctuations

Flame Region

C o m b u s to r

A i r

F u e l

I n l e t d u c t

F u e l f e e d l i n e

o

o

o

o

f

f

m

'mm

'm

m

'm'

1

Time evolution of disturbances responsible for the onset of instability

C o m b u s to r

A i r

F u e l

I n l e t d u c t

F u e l f e e d l i n e

t

t

t

t

t

t

a. Pressureat flame

b. Pressureat injector

modulation atinjector

d. Equiv. ratiofluct. at injector

e. Equiv. ratiofluctuation

at flame

f. Heat releaseoscillation

t

t

t

t

t

t

a. Pressureat flame

b. Pressureat injector

c. Fuel Mass flow modulation at

injector

d. Equiv. ratiofluct. at injector

e. Equiv. ratiofluctuation

at flame

f. Heat releaseoscillation

T

1

conv

TT

chem

Time evolution of disturbances responsible for the onset of instability (continued)

• From Rayleigh's Criterion an instability can occur if

1 + convect + chem=T/2, 3T/2, ...

• However:• If distance from injector to flame region is much shorter than a wavelength:

1/T<<1

• For low frequency instabilities:

chem/T<<1

• Thus, an approximate instability condition is:

convect /T= 1/2, 3/2, ...

• Conclusion: convect /T is a key parameter in combustor stability

Combustor Model• Linear Acoustics Model

– 1-D Wave solutions in fuel line and Regions i and iii:

ti)M1/(xikj

)M1/(xikjj e)eBeA('p jj

ti)M1/(xikj

)M1/(xikj

jjj e)eBeA(

c

1'v jj

– Boundary Conditions:• Combustor Exit: compact choked nozzle• Upstream end of inlet duct: p'=0• Upstream end of fuel line: v'=0

– Matching Conditions:• Flow through fuel orifice: mf = Kor(P)1/2

• Acoustic Oscillation in Regions i and iii matched by integrating across the flame region which was assumed to be acoustically compact

e.g. without mean flow or area discontinuities:

R e g io n i R e g io n i i

R e g io n i i i

I n t e r f a c e 2

I n t e r f a c e 1

'Qp

1'u'u

'p'p

12

21

Combustor Model (continued)

• Linear Heat Release Model:

- Combustion process assumed to behave as a well stirred reactor (WSR)

- An expression for the linearized response of a WSR to inlet perturbations can be derived: Q' = 3'

• Linear Oscillation Model:

perturbation at fuel injector:

- Mixture assumed to convect with the mean flow with unchanged composition: '(x,t) = inj'exp(i(t-x/u))

• Solution determines the complex frequency =r+ii

o

o

f

f

m

'm

m

'm'

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.070.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

convect/T

i/

r

Model Results

Stable Region

Unstable Region

Measured Instability regions

Model Results - Influence of Convective Time Delay on Combustor Stability

• Model Results are in good agreement with experimental data from DOE - FETC (Richards and Janus, ASME paper # 97-GT -244, Straub and Richards, ASME paper # 98-GT-492)

Choked fuel injector, p’=0 B.C. at inlet

Parameter Ranges:

= 40, 60, 80 m/s

Laf = 0-0.15 m

=0.6-1

u

Incorporating Effects of Flame Structure

• Time lag between ‘ at flame base and Q’, eq:

– Depends on structure of flame region and Stflame=fLflame/U:

– Modifies instability criterion: conv,eff/T = (convect+eq)/T=Cn

Spatial dependence of ’

Spatial dependence of p’

M

/2

Lconvect Lflame

Incorporating Effects of Flame Structure

Corresponding Flame Shape

Conclusion: Structure of flame region may have significant effects on stability behavior!

“

conv

,eff/T

Flame Strouhal #0 0.5 1 1.5 2 2.5 3

0.75

0.90

1.05

1.20

1.35

1.5

Unstable Regionconvect/T

Lflame= Lconvect

Lconvect

Lflame

-0.05

-0.03

-0.01

0.01

0.03

0.05

0.070.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

conv,eff/T

i/

r

Model Results

Stable Region

Unstable Region

Effects of Flame Structure on Stability Regions

• If assume conical flame where Lflame=Lconvect/2, Stflame<<1, predicted and measured regions agree almost perfectly

Choked fuel injector, p’=0 B.C. at inlet

Parameter Ranges:

= 40, 60, 80 m/s

Laf = 0-0.15 m

=0.6-1

u

Incorporating Effects of Flame Structure

• Not meaningful to correlate data with convect/T when significant changes in:– Structure of flame region

– Flame Strouhal number

• May explain recent data taken at DOE (Richards, Straub, Yip, Woodruff, Proc. 1998 AGTSR Combustion

Workshop)

Summary and Conclusions

• Combustion instabilities in LP combustors appear to be due to large heat release rate oscillations induced by oscillations

– In agreement with experiments at– U.Cal. - Berkeley (Mongia, Dibble and Lovett)

– DOE - FETC (G. Richards)

– Georgia Tech (to be reported at AIAA meeting, Jan. 1999, Reno, NV)

– UTRC (T. Rosjford)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9

convect/T

Rel

ated

to

p'/p

Pressure Amp. (630 Hz.)

Pressure Amp. (430 Hz.)

Recent Result from Georgia Tech Facility

Predicted Region

Summary and Conclusions

convect/T is a key parameter in describing combustor instability regions due to this mechanism

– Determining “effective” convect/T can be more difficult for longer flame regions

• Combustion instabilities could be suppressed by designing combustor parameters to be outside of instability ranges

• e.g., as demonstrated by Solar Turbines

(Steele, Rob, Proc. 1998 AGTSR Combustion Workshop)

Formation of Equivalence Ratio Oscillations

• Significant oscillations may form in inlet section

• Acoustic oscillation of 1%, gives oscillation of 20%! (choked fuel flow, M=0.05)

• Presence of oscillations during instability recently confirmed by Mongia, Dibble, and Lovett

(“Measurement of Air-Fuel Ratio Fluctuations Caused by Combustor Driven Oscillations," ASME paper 98-GT-304).

o

o

o

o

f

f

m

'mm

'm

m

'm'

1

C o m b u s to r

A i r

F u e l

I n l e t d u c t

F u e l f e e d l i n e

Results of a well-stirred reactor (WSR) model

• Unsteady WSR model subjected to perturbations in the inlet .

• Response of the unsteady rate of reaction increased as much as 200 times as was decreased from stoichiometric to lean mixtures

• Conclusion: oscillations induce strong heat release oscillations that can drive combustion instabilities under lean conditions

1.8

1.9

2

2.1

2.2

2.3

2.4

2.5

2.6

0.7 0.8 0.9 1Equivalence Ratio

Rea

ctio

n R

ate

(arb

itrar

y un

its)

From Lieuwen, T., Neumeier, Y., Zinn, B.T., Comb. Sci. and Tech, Vol. 135, 1-6, 1998.

Combustion Process Response Model

Using a global kinetic mechanism for propane and a WSR residence time of .1 ms.

0

0.2

0.4

0.6

0.8

1

1.2

0.5 0.6 0.7 0.8 0.9 1

Equivalence Ratio

(Q

'/Q)/

('

)

Combustor Model

R e g io n i R e g io n i i

R e g io n i i i

I n t e r f a c e 2

I n t e r f a c e 1

- A model was developed to predict the linear stability limits of the observed longitudinal combustion instabilities based on this mechanism

Fuel Line- Orifice Dynamics

Orifice Pressure drop = 2 atm., Combustor Pressure =10 atm., Fuel line Mach # = .05

0

0.5

1

1.5

2

2.5

3

3.5

0 0.2 0.4 0.6 0.8 1

Lfuel/Acoustic Wavelength

Ma

gn

itu

de

0

100

200

300

400

500

600

700

Ph

as

e

Magnitude

Phase

Model Results- Effect of Fuel Injector Location on Combustor Stability

Mean flow velocity = 40 m/s 80 m/s

StableUnstable

convect/T3/2 convect/T1/2 convect/T1/2

0 0.05 0.1 0.150.6

0.7

0.8

0.9

1

Fuel Injector Location, Laf

Eq

uiv

alen

ce R

atio

0 0.05 0.1 0.150.6

0.7

0.8

0.9

1

Fuel Injector Location, Laf

Eq

uiv

alen

ce R

atio

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

0.6

0.64

0.68

0.72

0.76

0.8

0.84

0.88

0.92

0.96

1

Fuel Line Length (Lfuel)

Eq

uiv

alen

ce R

atio

Model Results- Effect of Fuel Line Dynamics on Combustor Stability

• Combustor stability altered when unstable wavelength matches the fuel line length• This suggests a variable length fuel line as a passive control approach

StableUnstable

Lfuel/1/2 Lfuel/1 Mean flow

velocity = 40 m/s

Laf = 0.08 m